Path-integral calculation of the two-dimensional4Hephase diagram

Abstract

Path-integral Monte Carlo simulations have been used to determine the phase diagram of a two-dimensional ${}^4\mathrm{He}$ film in a range of temperatures and coverages where it undergoes solidification, superfluidity, and a liquid-gas transition $(0.25\mathrm{}\mathrm{K}<~T<~1.5\mathrm{K}\hspace{0.5em}0<\mathrm{}\sigma <0.094\mathrm{}\hspace{0.5em}{\AA }^{-2}).\mathrm{}$ We determine the phase-transition densities and give the coefficients for a functional form of the free energy in the liquid, solid, and gas phases. The phase diagram is similar to the one determined from experimental measurements of a second layer of helium on graphite.